The present invention relates to a device and a method for measuring sectional forces on a single-piece structural element with respect to a sectional plane by means of a plurality of strain gauges, wherein the structural element has a first and a second outer wall, which run perpendicular to the sectional plane, extend in a mirror-symmetrical manner in relation to each other about a first mirror plane of symmetry and are connected by further outer walls, wherein the first mirror plane of symmetry extends perpendicularly to the sectional plane, wherein each strain gauge has a measurement direction, and the electrical resistance of the strain gauge is a function of the length of the strain gauge in the measurement direction, wherein a first and a second strain gauge of the plurality of strain gauges are arranged on the first outer wall, and a third and a fourth strain gauge of the plurality of strain gauges are arranged on the second outer wall, wherein the strain gauges are arranged such that, when the structural element is loaded with a first force acting parallel to the sectional plane and parallel to the first mirror plane of symmetry, the first and third strain gauges undergo an identically oriented change in length in the measurement direction, the second and fourth strain gauges undergo an identically oriented change in length in the measurement direction, and the change in length of the first and third strain gauges is converse or opposite to the change in length of the second and fourth strain gauges.
By a sectional force or sectional magnitude or sectional reaction is meant the action of forces and torques within a structural element or component. These are the forces that must be applied or brought up by a structural element in order not to fail under the action of external forces or torques. Sectional forces or, also, sectional reactions, cannot be viewed from outside a structural element. In order for the forces and torques acting in the structural element to be made visible, a structural element must be notionally cut along a sectional plane, hence the name. Sectional forces become externally visible as a result of deformations of the structural element subjected to the action of a force or torque. The deformation of a structural element is manifested on its surface, in that the surface—depending on an acting force or acting torque and as a function of the location under consideration—undergoes stretching or compression.
The surface changes in the form of elongations or compressions can be measured by means of so-called strain gauges. A strain gauge is an electrical resistor, the resistance value or, simply, resistance, of which depends on the length of the strain gauge in the measurement direction. If the strain gauge is elongated, i.e. its length becomes greater in the measurement direction, then the electrical resistance of the strain gauge increases. Conversely, the electrical resistance of the strain gauge decreases when the strain gauge becomes compressed or shorter. Strain gauges are designed such that they have an unambiguous measurement direction, or measurement axis, which is characterized in that the change in resistance upon a change in length in the measurement direction, or along the measurement axis, is much greater than upon a change in length in other directions. In particular, strain gauges are preferably constructed such that a change in length perpendicular to the measurement direction results only in a minimal change in resistance.
In order to measure the elongation or compression of a surface of a structural element, the strain gauge is fixed to the surface in a suitable manner. If a force then acts on the structural element, and the surface of the structural element deforms in the region in which the strain gauge is arranged, the electrical resistance of the strain gauge changes. The change in the resistance is obviously greatest in the case when the surface of the structural element deforms parallel to the measurement direction of the strain gauge. It must be taken into consideration, however, that a structural element that is elongated perpendicular to the measurement direction of a strain gauge is normally compressed in the direction of the strain gauge. An elongation of the surface of a structural element in one direction therefore normally results in a measurable compression of a strain gauge the measurement direction of which runs perpendicular to the direction of elongation.
The length of the strain gauge therefore does not only change when the surface of the structural element is elongated parallel or perpendicular to the measurement direction of the strain gauge. In order to be able to determine the direction of an elongation or compression of the surface, several strain gauges, the measurement directions of which are oriented in differing directions, are attached one above the other or close to one another on the same surface. With a suitable arrangement of the strain gauges, the direction of the elongation of the surface of the structural element can be determined from the change in resistance of the various strain gauges.
This, however, is not sufficient for determining whether the deformation is produced by a force or a torque. For this purpose, distributed arrangements of preferably four strain gauges are used, of which two are compressed and two are elongated in each case when a particular force or a particular torque acts on the structural element. Preferably, the strain gauges are arranged such that different strain gauges are elongated or compressed, depending on whether the torque or the force is acting on the structural element.
Likewise, the state of the art has for a long time included the determination of the resistance of the strain gauges. Measurement of the electrical resistance is preferably not effected directly, but by means of a so-called Wheatstone bridge, or Wheatstone measuring bridge. An example of a Wheatstone bridge 1 is represented in FIG. 1. The Wheatstone bridge comprises four resistors 3, 5, 7, 9. A first resistor 3 and a second resistor 5 are connected in series. A supply voltage 11 drops across the first and the second resistor 3, 5. A third resistor 7 and a fourth resistor 9 are likewise connected in series and in parallel to the first and the second resistor 3, 5, such that the supply voltage 11 also drops across the third and the fourth resistor 7, 9. Furthermore, the Wheatstone bridge 1 comprises a voltmeter 13, which measures the voltage drop between a node in the connection of the first and the second resistor 3, 5 and a node in the connection of the third and the fourth resistor 7, 9. The voltmeter 13 does not measure any voltage drop precisely when the ratio of the first resistance 3 to the second resistance 5 corresponds to the ratio of the fourth resistance 9 to the third resistance 7. Measurable voltage drops, from which the magnitude of the change in resistance can be determined, occur on the voltmeter 13 already if there are even small changes in one of the resistances 3, 5, 7, 9. The precise mode of operation of the Wheatstone bridge 1 and the calculation of the changes in resistance are sufficiently known in the state of the art, and are therefore not discussed further here.
As is already evident from the above representation, the Wheatstone bridge is eminently suitable for determining the changes in resistances. Preferably, therefore, in a structure for measuring sectional forces, four strain gauges are used, which are coupled such that even a slight change in the length of the four strain gauges, and therefore in their resistances, relative to one another, results in as large as possible a voltage drop on the voltmeter. If, for example, a force results in the surface of a structural element undergoing elongation in one direction and compression in the direction perpendicular to the latter, then, for the purpose of observing the effect of this force, two strain gauges are preferably arranged such that their measurement direction extends parallel to the direction of elongation, and two strain gauges are arranged such that their measurement direction lies parallel to the direction of compression. In the case of the exemplary embodiment of a Wheatstone bridge represented in FIG. 1, the strain gauges that correspond to the first and third resistors 3, 7 would be arranged, for example, such that they undergo stretching, and the strain gauges that correspond to the second and fourth resistors 5, 9 would be arranged such that they undergo compression. Then, owing to the action of force, even small changes in the surface of the structural element result in measurable drops in voltage across the voltmeter 13.
However, such an arrangement is not necessarily advantageous, since, for example, a force and a torque acting perpendicular to the force can cause a change of length of the four strain gauges in the same direction. In other words, it is not possible to determine whether the change in resistance has been caused by the torque or by the force. It can therefore be advantageous to arrange the strain gauges at an angle in relation to a preferred direction of elongation, with the result that, upon action of the force that is to be observed, for example the first and third strain gauges undergo elongation and the second and fourth strain gauges undergo compression and, upon action of the torque on the structural element, the first and fourth strain gauges undergo elongation and the second and third strain gauges undergo compression. If the relative changes in magnitude of the electrical resistances of the strain gauges are equal in both cases, then, in the case of the described interconnection of the strain gauges, there is a voltage drop across the voltmeter only when the force is acting on the structural element. Under the action of the torque, by contrast, the ratio of the resistances does not alter, with the result that there is no voltage drop across the voltmeter. Such circuits are sufficiently known from the state of the art.
In any case, however, it is to be noted that the resolution of the Wheatstone bridge is limited with regard to the magnitude of the changes in resistance. In the case of particularly stiff structural elements made of stretch-resistant materials, the change in the length of the strain gauges is often so slight that they cannot be measured even with a Wheatstone bridge. However, precisely in the case of components subjected to large loads, and above all also to varying loads, over long periods of time, it is important to be able to determine with precision the forces and torques acting on the structural element or component. This is not possible with sufficient certainty by means of the arrangements known from the state of the art.